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Simplifying 5(1 + 2n) + -2(3 + -3n) = 1 + 6n + 9n (1 * 5 + 2n * 5) + -2(3 + -3n) = 1 + 6n + 9n (5 + 10n) + -2(3 + -3n) = 1 + 6n + 9n 5 + 10n + (3 * -2 + -3n * -2) = 1 + 6n + 9n 5 + 10n + (-6 + 6n) = 1 + 6n + 9n Reorder the terms: 5 + -6 + 10n + 6n = 1 + 6n + 9n Combine like terms: 5 + -6 = -1 -1 + 10n + 6n = 1 + 6n + 9n Combine like terms: 10n + 6n = 16n -1 + 16n = 1 + 6n + 9n Combine like terms: 6n + 9n = 15n -1 + 16n = 1 + 15n Solving -1 + 16n = 1 + 15n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15n' to each side of the equation. -1 + 16n + -15n = 1 + 15n + -15n Combine like terms: 16n + -15n = 1n -1 + 1n = 1 + 15n + -15n Combine like terms: 15n + -15n = 0 -1 + 1n = 1 + 0 -1 + 1n = 1 Add '1' to each side of the equation. -1 + 1 + 1n = 1 + 1 Combine like terms: -1 + 1 = 0 0 + 1n = 1 + 1 1n = 1 + 1 Combine like terms: 1 + 1 = 2 1n = 2 Divide each side by '1'. n = 2 Simplifying n = 2
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